Having her own band goes to her head (5)
I believe the answer is:
alice
'having her own band goes' is the definition.
I can't judge whether this definition defines the answer.
'her head' is the wordplay.
'her' becomes 'Ali'.
'head' becomes 'ce' (I can't justify this - if you can you should give a lot more credence to this answer).
'ali'+'ce'='ALICE'
'to' acts as a link.
Can you help me to learn more?
(Other definitions for alice that I've seen before include "Girl famed for Wonderland adventures" , "She ate the "Eat Me" and drank the "Drink Me"" , "Movement" , "Girl famous for entering Wonderland" , "Lewis Carroll character" .)